1. Field of the Invention
The present invention relates to a method for performing absolute calibration measurement of wavefronts and an absolute calibration apparatus used for interferometric measurement of precision surfaces such as planes and spheres and a method of synthesizing wavefronts used for measurement of large diameter planar, spherical, or aspheric surfaces.
2. Discussion of the Related Art
A wavefront generation extraction computation method is described in Japanese Patent Laid-open Publication H7-043125, which is hereby incorporated by reference, that focuses primarily on algorithms for extracting rotationally symmetric components. In particular, the chief objective of the method is the removal of the effects of environmental disturbances by applying the rotationally symmetric component of the data, which is essentially contour in nature, to all of the lateral shift subtraction data.
In the wavefront generation extraction computation method, however, there is a problem in that if there is too much aberration in the reference wavefront, the best approximation sphere (plane) of the reference standard surface becomes severely tilted, inevitably introducing rotationally symmetric component extraction errors.
A conventional wavefront synthesis method makes partial measurements, joining the data piece by piece. This joining process creates areas in which large-diameter spherical surfaces overlap with each other. To collect data in this manner for an entire sphere, the method relies on the fact that overlap areas in the data from the partial measurements are essentially equal. A conventional apparatus for this wavefront synthesis method is disclosed in Japanese Patent Laid-Open Publication No. 5-40024, which is hereby incorporated by reference.
The synthesizing wavefronts method performs operations in which multiple sets of different interferometric measurement data are joined together. Normally, best-fit curve-fitting (of which the least squares method is a representative type) is performed to compensate for variances contained in the sets of measurement data.
If there are shape errors in the reference surface (in a Fizeau interferometer, the Fizeau surface) or there are lateral coordinate errors, since these errors tend to skew the data, the above assumption that the shapes of the overlap areas are essentially equal no longer holds true. Therefore, the partial measurement data does not fit together well, even when statistical techniques such as best-fit curve fitting are used. This point is considered further below.
FIG. 15 illustrates interferometric measurement of a test surface (a plane). The interferometer used here is a Fizeau interferometer, but the type of interferometer is not important. Since the wavefront synthesis can work if there are at least two sets of partial measurement data, the explanation assumes two sets of data.
We will use a planar surface as the test surface to simplify the explanation. When the test surface is a spherical or aspheric surface, there is an increase in error factors associated with "alignment error corrections" (computations to correct for apparent errors that occur due to alignment factors that always exist in interferometers).
As shown in FIG. 15A wavefronts from the test surface 1a of a test object 1 and the Fizeau surface 2a of the Fizeau flat 2 are caused to interfere. Then by applying an alignment error correction (tilt, for a planar surface) to the resulting interference pattern obtained, shape error (flatness) data is obtained for the test surface 1a, with Fizeau surface 2a as the reference surface (the surface that serves as the standard against which the shape error of the test surface is judged). We will designate this data as the "first partial measurement data."
The test surface 1a is then shifted laterally, as shown in FIG. 15B, and another interferometer measurement is performed in the same manner. The data from this measurement is designated the "second partial measurement data." In FIG. 15B, a marking, "P," is placed on the test area 1 to make it easier to visualize its lateral movement state.
FIG. 15C shows the two sets of partial measurement data joined, with this marking "P" as the reference. Moreover, in actual measurements, in order to make it possible to superimpose the two sets of partial measurement data, even when the object is rotated the test object 1 by lateral movement a minimum of two markings on the test surface 1a, or the equivalent thereof in measurement control, are required. Additionally, if there is a change in the magnification factor of the data for each partial measurement (the equivalent of zooming on the data) a minimum of two markings on the test surface 1a, or the equivalent thereof in measurement control, are required.
It is a common practice, in high-precision interferometric measurements, to perform "reference subtraction." This is done to avoid the labor-intensive effort required to obtain a high-precision finish on the Fizeau surface and to avoid the influence of drift during measurement. Reference subtraction is a procedure that is performed just prior to taking the measurements on the test surface to calibrate the measurement wavefront incident to the test surface (hereinafter, the "reference wavefront") against a reference standard surface of even higher surface precision, by establishing interference between wavefronts of the Fizeau surface and the reference standard surface. When this "reference subtraction" is used, the function of the reference surface for the measurement is transferred from the Fizeau surface to the reference standard surface.
Because the reference standard surface is normally finished to a high level of precision, for the precision required for measurement of normal surfaces under test when data is not being joined, the absolute shape error of the reference standard surface itself can be ignored. When performing interferometric measurement of surfaces by the wavefront synthesis method, however, the overlap areas of the two sets of partial measurement data correspond to two different areas of the reference surface. In FIG. 15C, the reference surfaces, when the partial measurement data in FIG. 15A and FIG. 15B were obtained, are indicated by shading, with the shaded overlapping portion indicating the overlap of the partial measurement data.
As can be seen in FIG. 15D, the shape error of the Fizeau surface (reference standard surface) is not offset in the overlap area. Thus, even if a reference subtraction technique is used, the shape error of the reference standard itself will inevitably end up being superimposed on the interferometer data. Therefore, while the magnitude of the error may depend on the size of the overlap area and the precision of the reference standard surface, in this method, a certain amount of data-joining errors in best-fit curve fitting was unavoidable.
The data-joining errors also occur when the reference surface itself has lateral coordinate distortion. In general, a wavefront passing through a light-converging optical system receives primarily rotationally symmetric distortion. For example, if the area measured by the entire Fizeau surface could be specified, it would receive a standardized lateral coordinate distortion at the effective center of the Fizeau surface and the outer diameter as is shown in FIG. 15E. In this drawing, the solid line shows, along the vertical axis, the shift of positions of FIG. 15A measurement data points (positions on the test surface corresponding to pixels of the CCD imaging device of the interferometer). The horizontal axis represents the effective area of the Fizeau surface. The dotted line shows a similar curve plotted with the origin of the coordinate system of FIG. 15B as the reference. The fact that the signs (polarity) of the curves in FIG. 15E are different indicates that the positions of the data points are shifted in the opposite direction.
Both curves are for the case in which the center axis of the rotationally symmetric distortion passes through the origin of the coordinate system. The coordinate system origin is the computation origin for alignment error correction and can be taken as the center of the effective area of the Fizeau surface.
As shown in FIG. 15E, the sampling points in the two partial measurement areas of the test surface do not match, even if partial measurement data that has been corrected for reference surface shape error is used, for example, this will not offset the shape of the test surface. In addition, when the test surface is not a plane, there will be "geometric distortion" due to the different coordinate systems.